## Calculate value of variable from solution to a 2nd ODF

The Question:
Find the value of r such that v = xr is a solution of

xd2v/dx2 + (x+4)$\frac{dv}{dx}$ + 3v = 0

My Solution:

After finding the 1st and 2nd derivative of v and substituting into the equation to equat to zero and look for r, I get the answer r =-3. I also get a root that is undefined. I just want someone to confirm my answer or let me know if there is a better method to solve for r. Could their be a possibility of an error in the question?

Thanks

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 Quote by blondii The Question: After finding the 1st and 2nd derivative of v and substituting into the equation to equat to zero and look for r, I get the answer r =-3. Thanks
Just a little correction. After expanding the diff equation I get xr(rx-1+1)(3+r) = 0

The answers are r = -3, r = -x or r = undefined.

Please advise if I am on the right track.

Thanks

 You are on the right track. Be sure, however, to treat the cases where r = 1 and r = 2 separately; think about why you should :) On the other hand, what doe r = -x or undefined mean? r should be a value independent of x. And saying that r = undefined is undefined and has no meaning. So r = -3 is indeed the solution.

## Calculate value of variable from solution to a 2nd ODF

Thanks for the reply who. Much appreciated. Cheers

 Tags homogenous, second order odf